Shyvana The Half-Dragon

Active: Shyvana's next autoattack will strike twice in one swift movement. The second attack will deal physical damage equal to a percentage of her total attack damage. Both attacks will trigger on-hit effects.
Dragon Form: Twin Bite will damage all units in front of Shyvana when she uses her next autottack instead of just her target. Each unit hit will both trigger on-hit effects and grant FURY twice.
Shyvana's autoattacks against non-structures reduce the cooldown of Twin Bite by 0.5 seconds.
Second Strike Physical Damage: 80 / 85 / 90 / 95 / 100% AD
COOLDOWN: 10 / 9 / 8 / 7 / 6

Passive: While in Human Form, Shyvana passively generates FURY every 1.5 seconds. Shyvana's basic attacks generate 2 FURY, even in Dragon's Descent Dragon Form or against structures.
Active: Shyvana transforms into a dragon and dashes to a target location. Enemies along her path take magic damage and are pushed toward her target location.
While in Dragon's Descent Dragon Form, Shyvana's FURY decays at a rate of 5 per second. Once her FURY is depleted, she will return to her normal state. Dragon's Descent has no cooldown or initial cost but can only be activated when Shyvana has 100 FURY.
Fury gained per 1.5 seconds: 1 / 2 / 3
Magic Damage: 175 / 300 / 425 (+ 70% AP)
RANGE: 1000
COST: 5 fury per second

A CDR build

This build should be read as follows:
- against an AD in lane, build locket 1st as it will give you decent Health and Armor for its cost, plus a good shield (to help against ignite while a potion is running) and most needed CDR
-against an AP, build spirit visage to gain good MR, Health and CDR again
The aim of the first item is to get you extremely tanky at a low cost while still lv 6-8 thanks to your ultimate's passive Armor and MR boost
You'll be tough to kill, depsite only having a low cost item
Take spirit of the elder lizard then, to help push the wave and go steal some jungle camps (the Butcher's passive helps a lot) and the burning effect synergizes well with W, both in human and dragon form. You should have a lot of CDR, be level 11+ so you should be able to keep W constantly running. Additionnaly, 45 damage is a lot for only 2000 gold.
Then, it all depends on who's fed on the ennemy team. Get either a bulwark or a sunfire cape. the latter is the default item, if noone is particularily fed on the ennemy team. It will greatly help to survive during early teamfights and provide a LOT of passive AoE magic damage, with your W and the spirit of the elder lizard.
Then again, see what you need the most:
- more durability? take a randuin's
- more damage? go for blade of the ruined king, or if they're slippery, take a frozen maillet
IMPORTANT: this build focuses on early pressure, be sure to deny a lot of creeps to your opponent in lane, by pushing or harassing him (they'll realize soon that just standing next to you is painful). It contains a lot of CDR, to help get to the point where:
- Q has 3.6s cd
- W has 7.2s cd
- E has 3.6s cd
You should be able to keep W constantly in teamfights, keep the ennemy team's armor debuffed (E) and spamm Q to make up for the lack of attack speed in this build. It should help retain the dragon form and lessen the time between two ultimate as well as being extremely mobile.
Shyvanna doesn't need high resistance items early game as her ultimate provides some, so better focus on utility too, mainlyu cdr.
This build has proven to be quite effective, if you also manage to keep good vision on the map: be sure to buy wards, to help preventing ganks (as you'll be pushing a lot) and to be able to counter-jungle once you get the spirit stone.
NB: this build is very different from your usual shyvana build in season 2 where you would focus on attack speed. This is due to the fact that nowadays, most champions have a form of cc, mainly slows. AD carries are slippery as hell and don't even mention assassins. With this build, even if you don't attack that much, you should be able to deal significant amounts of damage by JUST BEING THERE as well a being extremely durable and useful to your team (locket+randuin+bulwark for instance, as well as the armor debuff).

Skillorder

Pretty standard skill order.
Level up W 1st, as it is your main source of damage and high mobility.
Then, level up E because it adds some on-hit MAGIC damage, to help keeping your damage mixed and thus building defenses against you harder. The base damage on the spell is nice too and the CD decreases so that you'll get your Q and E approximately at the same time (taking into account the reduced CD on Q for each attack).
Finally, level up Q, because apart from the reduced CD, it only adds 20% of your AD as damage which is lower than the E on-hit damage for each rank.
Take ultimate at level 6,11 and 16.

Summoner spells

Spells

Ignite

Flash

Alternate Spells Set

Pretty standard again.
It's up to the player's preference wether you take exhaust or flash.
With the item build in this guide, you should be able to get you ultimate quite often, so you might consider taking exhaust.
Nevertheless, don't forget that if, fr example, lee sin kicks you away after you ulted, or right when you ult, you'll be wasting a lot of time if you don't have flash/ghost.

Again, it's up to the player, but I take hybrid penetration marks to increase my damage, even though I will build defensive.
The rest is standard on Shyvana.
An laternate set can consist of health quint, hybrid pen marks, armor seals, cdr glyphs. For instance, against an ennemy olaf or darius (to help sustain the true damage), or another AD like Riven or Renekton, CDR runes help having more damaging sequences than them due to reduced CDs. The extra health help winning early trades.

Again, extremely defensive masteries, but you'll want to win trades based on your sheer tankiness and high base damage.
This tree helps making up for the "cheap" items you'll buy early game, such as the locket because, between the masteries and runes+locket+ultimate, you'll achieve a tankiness of the level of a randuin's maybe, but at a much lower cost, much earlier, while still getting the shield and the CDR as a bonus.